Electronic properties of a ferromagnetic shape memory alloy: Ni-Mn-Ga

1
Talk at Electronic Structure of Emerging
Materials Theory and Experiment at
Lonavala-Khandala, 8th February, 2007
Electronic properties of a ferromagnetic shape
memory alloy Ni-Mn-Ga
Sudipta Roy Barman
UGC-DAE Consortium for Scientific Research,
Indore
Part of university system fully funded by UGC.
Besides in-house research, we provide advanced
research facilities to University
researchers. Emphasis on Researchers in different
academic institutions to work together.
www.csr.ernet.in
Max Planck partner group project
2

What is a shape memory alloy?
SMA effect involves structural transition called
martensitic (after F. Martens) transformations
which are diffusionless. It is a first order
transformation and occurs by nucleation and
growth of a lower symmetry (tetragonal/orthorhomb
ic) martensitic phase from the parent higher
symmetry (cubic austenitic) phase.
3
Ni-Mn-Ga is ferromagnetic, and exhibits magnetic
SMA
SMA Transformation from the martensite to
austenite phase by temperature or stress. FSMA
Entirely within the martensite phase, actuation
by magnetic field, faster than conventional
stress or temperature induced SMA. 10 Magnetic
Field Induced Strain in Ni50Mn30Ga20 reported.
4
Live simulation of the FSMA effect
Rotation of magnetic moments Magnetocrystalline
anisotropyltlt Zeeman energy
FSMA effect change in shape Magnetocrystalline
anisotropygtgt Zeeman energy
10 Magnetic Field Induced Strain in
Ni50Mn30Ga20 reported. Highest in any system till
date.
5
Magnetic domains and twin bands
Topography image
MFM image
Magnetic force microscopy image of Ni2.23Mn0.8Ga
in the martensitic phase at room temperature
clearly shows the twin bands (width 10 micron)
and magnetic domains (width 2-3 microns)
C. Biswas, S. Banik, A. K. Shukla, R. S. Dhaka,
V. Ganesan, and S. R. Barman, , Surface Science,
600, 3749 (2006).
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Smart actuator materials
Potential fields of applications
7
A real actuator made from FSMA by Adaptamat
This demo is animated, but it shows the motion of
the axis. The actuator can be driven
faster/slower (average 70mm/s) and in
bigger/smaller steps (accuracy lt1µm).
8
The FSMA mechanism
Magnetic field induced strain 1- c/a
9
Overview of our collaborative work on study of
fundamental properties of Ni-Mn-Ga

• Polycrystalline ingot preparation in Arc
  furnace, EDAX In house
• Thermal, transport and magnetic studies
  Differential Scanning calorimetry, Ac
  susceptibility magnetization resistivity
  magnetoresistance AFM, MFM
• Collaboration SNBCBS,Kolkata Suhkadia
  University, Udaipur TIFR, Mumbai RRCAT, Indore
  In-house ? Phys. Rev. B, 74, 085110 (2006)
  Appl. Phys. Lett. . 86, 202508 (2005) Surface
  Science, 600, 3749 (2006).
• Structural studies X-ray diffraction
  Collaboration Banaras Hindu University, Banaras
  ? Phys. Rev. B (2006, in press) Phys. Rev. B
  (2007, in press)
• Electronic structure Photoemission spectroscopy
  (UPS and XPS) Inverse photoemission
  spectroscopy theory (FPLAPW) Collaboration
  In-house and CAT, Indore ? Phys. Rev. B, 72,
  073103 (2005) Phys. Rev. B 72, 184410 (2005)
  Applied Surface Science, 252, 3380 (2006)
• Compton scattering Collaboration Rajasthan
  University, Jaipur Sukhadia university, Udaipur,
  Spring-8, Japan ? Phys. Rev. B (2007), accepted.

10
Acknowledgments to the collaborators and funding
agencies
Phd students S. Banik, C. Biswas, and A. K.
Shukla RRCAT, Indore A. Chakrabarti UGC-DAE CSR,
Indore R. Rawat, A. M. Awasthi, N. P. Lalla, D.
M. Phase, A. Banerjee, V. Sathe, V.
Ganesan. Banaras Hindu Univeristy, Banaras D.
Pandey, R. Ranjan S.N. Bose Centre for Basic
Sciences U. Kumar, P. Mukhopadhyay Sukhadia
Univerisity, Udaipur B. L. Ahuja Rajasthan
univeristy, Jaipur B. K. Sharma
Department of Science and Technology, Govt. of
India through SERC project (2000-2005) and
Ramanna Research Grant. P. Chaddah and A. Gupta
11
Samples grown in house
Polycrystalline ingots of Ni-Mn-Ga alloys were
prepared by melting in Arc furnace. Appropriate
quantities of Ni, Mn, and Ga of 99.99 purity
melted under Argon atmosphere. 0.5 to 1 maximum
loss of weight, possibility of difference in
intended and actual composition. The L21 phase is
obtained after annealing at 1100K in sealed
quartz ampules. Annealing time for each sample
is more than a week to ensure homogenization.
The ingots were quenched in ice water.
12
Ni2MnGa is a Heusler alloy

• L21 structure Four interpenetrating f.c.c.
  sublattices with
• Ni at (1/4,1/4,1/4 ) and (3/4,3/4,3/4)
• Mn at (1/2,1/2,1/2),
• Ga at (0,0,0).

• Ferromagnetism due to RKKY indirect exchange
  interaction.
• Heusler alloys are famous for localized large
  magnetic moments on Mn.

13
Temperature dependent XRD evidence of modulation
Austenite
Martensite structure more complicated than
tetragonal! 7 layer (7M) modulation in 110
direction.
Ranjan, Banik, Kumar, Mukhopadhyay, Barman,
Pandey, PRB (2006).
14
Phase coexistence in Ni2MnGa
(a) Hysteresis curve showing mole fraction of the
cubic phase determined from Rietveld analysis of
the XRD patterns. (b) Ac-susceptibity
Decrease at TM due to large magnetocrystalline
anisotropy in martensitic phase. (c)
Differential scanning calorimetry
Nice agreement between structural, magnetic and
thermal techniques. Small width of hysteresis
14-38 K highly thermoelastic (mobile interface,
strain less).
15
Resistivity and magnetoresistance
T/Tc 0.8
Metallic behaviour with a clear jump at TM.
Ref M. Kataoka, PRB, 63, 134435 (2001)

• Highest known magnetoresistance at room
  temperature for shape memory alloys. For x0.35,
  MR is around 7.3 at 8T.
• Experimental MR behavior agrees with the
  theoretical calculation.
• Magnetic spin disorder scattering increases with
  increasing x.

C. Biswas, R. Rawat, S.R. Barman, Appl. Phys.
Lett., 86, 202508 (2005)
16
Total energy calculations using Full potential
linearized augmented plane wave (FPLAPW) method

• Total energy includes the electron kinetic
  energy and electron-electron, electron-nuclear
  and nuclear-nuclear potentials.
• Ab-initio i.e. no requirement of input
  parameters.
• FPLAPW solves the equations of density
  functional theory by variational expansion
  approach by approximating solutions as a finite
  linear combination of basis functions. What
  distinguishes the LAPW method from others is the
  choice of basis.

Ref www-phys.llnl.gov/Research/Metals_Alloys/Meth
ods/AbInitio/LAPW/
WIEN code (P. Blaha, K. Schwartz, and J. Luitz,
Tech. Universität, Wien, Austria, 1999)
17
Structure optimization for Ni2MnGa
Experimental c/a 0.94. Previous theory c/a
1.2, 1, etc.
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Total energy contours for structural optimization
of Ni2MnGa

• For ferromagnetic martensitic phase, a 5.88 ?
  and c 5.70 ?, with c/a0.97. Comapres well with
  expt. c/a0.94.
• Good agreement with experimental lattice
  constants a 5.88?, c 5.56 ? within 2.5.
• Tetragonal phase more stable than the cubic phase
  by 3.6 meV/atom.

Barman, Banik, Chakrabarti, Phys Rev B, 72,
184410 (2005)
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Ni2MnGa ? Ni-Mn-Ga
Increase Nickel Ni2MnGa ?
Ni2xMn1-xGa (Ni?, Mn?) ? Ni3Ga (x1)
Increase Manganese Ni2MnGa ?
Ni2-yMn1yGa (Mn?, Ni?) ? NiMn2Ga or Mn2NiGa
(y1)
20
Structure optimization for Ni2.25Mn0.75Ga
Good agreement between the experimental and
theoretical lattice constants Expt a 5.439 ? ,
c 6.563 ? Theory a 5.38 ?, c 6.70 ?) within
1 for a and 2 for c.
21
Phase diagram of Ni2xMn1-xGa
P paramagnetic, F ferromagnetic
C cubic (austenite), T tetragonal (martensite)
x

• TC and TM determined by DSC and ac-chi
  measurements.
• TC increases with Ni content i.e. x.
• TC TM for x 0.2, large magnetoelastic
  coupling and gaint magnetocaloric effect.
• TC lt TM for xgt 0.2, emergence of the new
  paramagnetic tetragonal phase, confirmed by high
  temperature XRD.

Banik, Chakrabarti, Kumar, Mukhopadhyay,
Awasthi, Ranjan, Schneider, Ahuja, and Barman,
PRB, 74, 085110 (2006)
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Phase diagram vis-à-vis total energies
x 0.25, Ni2.25Mn0.75Ga
x 0, Ni2MnGa
TMgtTC
TMltTC
PC
PC paramagnetic cubic FC ferromagnetic
cubic FT ferromagnetic tetragonal PT
paramagnetic tetragonal Total energies in meV/
atom
PC
39
PT
322
253
219
kBTC Etot(P) - Etot(F) ? Decrease in TC for x
0.25
FC
3.6
FT
FT
kBTM Etot(C) - Etot(T) ? Increase in TM for x
0.25
23
Experimental facilities for electronic structure
studies
IPES spectrometer
XPS/UPS spectrometer
S. Banik, A. K. Shukla and S.R. Barman, RSI, 76,
066102 (2005).
24
UPS VB of Ni2MnGa compared to VB calculated from
DOS
Calculated DOS
Non-modulated
Modulated

• Good agreement between expt. and theory VB
  dominated by Ni 3dMn 3d hybridized states.
• Ni 3d states with peak at 1.75 eV. Mn 3d states
  exhibit two peaks at 1.3 eV and 3.1 eV.
• VB for non-modulated structure in better
  agreement with expt. So, influence of modulation
  diminishes at the surface.
• Mn 3d dominated peak above EF.

Chakrabarti, Biswas, Banik, Dhaka, Shukla,
Barman, PRB, 72, 073103 (2005)
25
Ni2xMn1-xGa effect of excess Nickel
Ni clustering, formation of Ni1 3d Ni2 3d
hybridized states at expense of Ni 3d Mn 3d
hybridized states.
26
Unoccupied states of Ni2xMn1-xGa
Difference between expt. and theory Mn related
peak is shifted by 0.4 eV. Indicates existence of
self energy effects.
Mn
Ni
As x? Ni peak intensity increases and Mn
decreases. Small shift of Mn peak to higher
energies.
27
Magnetic moments of Ni2MnGa

• Saturation magnetic moment of Ni2MnGa
• MCP 4 mB
• Magnetization 3.8 mB
• FPLAPW 4.13 mB
• Large magnetic moments on Mn, clear from spin
  polarized DOS.
• Ni moment 10 of Mn, both aligned in same
  direction.
• Decrease in saturation magnetization with
  increasing x.

B. L. Ahuja, B. K. Sharma, S. Mathur, N. L. Heda,
M. Itou, A. Andrejczuk, Y. Sakurai, A.
Chakrabarti, S. Banik, A. M. Awasthi and S. R.
Barman, Phys. Rev. B (accepted).
28
Magnetic moments of Mn2NiGa
Increase Manganese Ni2MnGa ? Ni2-yMn1yGa (Mn?,
Ni?) ? NiMn2Ga or Mn2NiGa (y1)
Mn2NiGa Ni (0.25,0.25,0.25) Mn1 (0.75,
0.75, 0.75) Mn2 (0.5, 0.5, 0.5) Ga
(0,0,0) TC375K, TM260K
Spin density in 110 plane
Charge density in 110 plane
The Mn atom in Ni position (Mn1) is
antiferrimagnetically aligned to the original Mn
(Mn2) and the total moment decreases. Reason for
opposite alignment is direct Mn-Mn interation.
The nearest neighbours of Mn1 atoms are four Mn2
and four Ga atoms at a distance of 2.53Å.

• Ni2MnGa Four interpenetrating f.c.c.
  sublattice
• Ni at (0.25,0.25,0.25) and (0.75, 0.75, 0.75)
• Mn at (0.5, 0.5, 0.5),
• Ga at (0,0,0).

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Why Mn1 and Mn2 magnetic moments are different?
Martensite Austenite
Mn1 -2.21 -2.43
Mn2 2.91 3.2
Ni 0.27 0.32
Total 1.21 1.29
Strong hybridization between the down spin 3d
states of Ni and Mn2 (n.n. 2.55Å) compared
to Weaker hybridization between the up spin MNi
and Mn1 3d states (2.73 Å)
30
Origin of the structural transition (the
martensitic phase)
intensity
Lowering of the electron states related to the
cubic to tetragonal structural transition Jahn
Teller effect (Fujii et al., JPSJ)
kinetic energy
31
Origin of the modulated phases in Ni2MnGa Fermi
surface nesting
If the Fermi surface (FS) has flat parallel
portions i.e. if it is nested with nesting vector
(vector joining the parallel portions of the FS),
a pronounced phonon softening can occur at q
resulting in a modulated pre-martensitic or
martensitic phases.
Bungaro, Rabe, Dal Corso, PRB, 68, 134104, (2003)

Cross section of the Fermi surface (a) with the
(001) plane. The arrows are examples of nesting
vectors q00.34(1,1,0).
(a) Minority spin Fermi surface of cubic Ni2MnGa.
32
Highly nested FS of Mn2NiGa
010
100
Minority spin hole type FS, Band 27, NV
0.4100,NA 0.17 a.u.2
Majority spin FS, band 29 NV 0.44(100) (010)
Minority spin FS, Band 29 NV q1
0.311,0,0NA(q1) 0.164a.u.2 NV q2
0.46(1,1,0) NA 0.034a.u.2
33
Conclusions
I hope I could give you a flavour of this
important material . We will appreciate your
suggestions and comments that might lead to new
collaborations.. Thank you for your attention.

• Phase diagram determined from TM and TC
  variation as function of Ni excess (x). For xgt
  0.2, martensitic transition occurs in
  paramagnetic phase.
• Phase co-existence shown, existence of a 7 layer
  modulated structure at low temperature for
  Ni2MnGa.
• Ni2MnGa shows large negative magnetoresistance
  (7) at room temperature due to s-d spin
  scattering.
• Structure from total energy calculations,
  magnetic moments, occupied VB are in good
  agreement with experiment.
• Self energy effects in unoccupied DOS.
• Evidence of Ni cluster formation with Ni
  doping.
• Origin of structural transition related to
  lowering of total energy redistribution of
  states near EF.
• Antiferrimagnetism in Mn2NiGa
• Highly nested Fermi surface

34
Ni 2p of Ni2MnGa shows an interesting satellite
feature

• Satellite feature at 6.8 eV and 5.9 eV below Ni
  2p3/2 and 2p1/2 peak respectively.
• Satellite feature in Ni metal at 6 eV and 4.6 eV
  below Ni 2p3/2 and 2p1/2 peak respectively.
• Band filling, Udc and 3d bandwidth are
  responsible for the binding energy shift of the
  main peak, satellite and decrease in satellite
  intensity.

35
Mn magnetic moment from XPS

• Exchange splitting
• Occurs when the system has unpaired electrons in
  valance band.

• Exchange split peak is at
• 1167 eV (x0, Austenite), ?Eex 4.3 eV ??
• 1166.2 eV (x0, Martensite), ?Eex 5.1 eV
• 1166.5 eV (x0.1, Martensite), ?Eex 4.8 eV
• 1166.9 eV (x0.2, Martensite). ?Eex 4.4 eV
• Mn moment decreasing with decrease in Mn content.
• From theory 3.4 mB (Fuji et al., JPSJ), 3.36 mB
  (Ayuela et al.JOPCM)

36
Origin of satellite in Ni core level

• The partially filled d states are treated as
  non-degenerate state interacting with s
  conduction states through s-d hybridization and
  with d states of other atoms through d-d transfer
  interaction giving rise to narrow d-band.
• This initial mixing gives 3d94s ground state of
  Ni.

EF

• If screening is better main peak, no satellite.
• If screening is poor satellite arises.

3d9
3d10
4s
Excited state
Ground state
hn
2p
c
-1
37
Microscopic twin structure with field
Ref Pan et. al. JAP. 87, 4702 (2000)
Magnetic domains and twin bands clearly observed.
MR explained by twin variant rearrangement with
field.
Magnetic force microscopy image of Ni2.23Mn0.8Ga
in the martensitic phase at room temperature.
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Actuator
An actuator produced by AdaptaMat which controls
pressure in a pneumatic valve.
When magnetic field is applied, the MSM element
elongates in the direction perpendicular to the
magnetic field.
41
Crystal structure at room temperature
Martensi te
Austeni te
Martensitic phase at room temperature.
42
Lattice constant variation with x in Ni2xMn1-xGa
The spontaneous strain increases from 17.6 to
23 between x 0.15 and 0.35. Linear variation of
lattice constants in alloys can be explained by
Vegards law, This is expected because both Ni
and Mn are 3d elements with similar electronic
configuration and small size difference.
43
DSC and ac-susceptibility of Ni2xMn1-xGa
x 0
x 0.24
x 0.35
x Ms (TM) Mf As Af
0 205 189 216 234
0.24 434 408 423 447
0.35 537 523 553 582
DSC Rate 10 C/min
Susceptibility 26 Oe field, 33.33 Hz
Albertini et al, JAP, 89 5614, 2001
Small width of hysteresis 14-38 K for x0 highly
thermoelastic (mobile interface, strain
less). Decrease of c at TM due to large
magnetocrystalline anisotropy in martensitic
phase. For xgt0.2 TMgtTC change in c shape.
Banik, Chakrabarti, Kumar, Mukhopadhyay,
Awasthi, Ranjan, Schneider, Ahuja, and Barman,
PRB, 74, 085110 (2006)
44
Structure and magnetization of x 0.35
Magnetization versus field M-H hysteresis loop at
293 K, the region close to H0 is shown in the
inset.
45
Photoemission (PES) and Inverse photoemission
spectroscopy (IPES)
PES
IPES
46
Characteristics of our PES workstation
Characteristics PES station Our aim..
Angle dependent XPS Yes
Angle resolved PES No Yes, using angle resolved analyzer
Base pressure 6 x 10-11 mbar
LEED Not available Yes
Analyser energy resolution in UPS 100 meV 1 meV
Analyzer energy resolution in XPS 0.8 eV 0.4 eV (by monochromatic XPS)
Spatial resolution 100 mm lt10 mm
Temperature of expt. 150 K, RT lt15 K to RT (controlled)
47
The Inverse Photoemission Spectrometer work
station

• Photon detector and electron gun fabricated,
  interfaced with Labview
• Two level Mu metal (Ni77Fe15CoMo) chamber.
• Sample heating up to 950C.
• Indigenous design and assembly of the entire
  system involving purchase of more than 100
  different items from 25 companies.

Gas filled photon detector
Operating principle
Design
S. Banik, A. K. Shukla and S.R. Barman, RSI, 76,
066102 (2005).
48
Surface composition from XPS for sputtered surface
Ni 3p

• EDAX Ni2.1Mn0.88Ga1.01
• Sputtering
• 0.5 keV Ni2.6Mn0.4Ga0.99.
• 3.0 keV Ni2.45Mn0.4Ga1.1.
• Sputtering yield of Ni is less than Mn and Ga
  For 0.5 keV Ar ions, Ni (1.3 atoms/ion) and
  Mn(1.9 atoms/ion)

Ga 3d
Mn 3p
Ion sputtering increases Ni content on the
surface.
49
Surface composition from XPS with annealing
T (0C) Surface Composition (20 A0)
100 Ni2.47Mn0.44Ga1.09
200 Ni2.42Mn0.5Ga1.09
300 Ni2.25Mn0.71Ga1.03
350 Ni2.14Mn0.76Ga1.1

• With increasing annealing temperature Mn
  segregates to surface.
• At about 390oC the NiMn ratio is same as that of
  the bulk (2.3).

50
Valence band spectrum of Ni2MnGa in martensitic
phase
51
DOS calculation using the actual modulated
structure
Non-modulated
7 layer modulated phase, Pnnm space group, 56
atoms/unit cell, a4.215, b29.302 and c5.557 Å.
Modulated
52
Comparison photoemission and theory
Cu2MnAl
D. Brown et al., PRB, 57, 1563 (1998)
Disagreement in Feature A. Could overall
agreement be better if modulation is considered?
53
Self energy effects in Ni2MnGa IPES
The states near EF are broader and the 1.9-eV
peak is shifted toward higher energy by 0.4 eV
w.r.t.calculated spectrum. These differences
could be related to existence of correlation
effects. DFT is a ground-state calculation and
the electron-electron interaction is considered
in an average way. Deviation from DFT is
quantified in terms of self-energy, where the
real part gives the energy shift and the
imaginary part gives the broadening. Self energy
effects in the unoccupied states have also been
observed in 3d transition metals like Cu.
Inverse photoemission spectrum of Ni2MnGa at
room temperature in the FC phase, compared with
the calculated conduction band of Ni2MnGa FC
phase based on total, Mn, and Ni 3d PDOS. The
IPES spectrum of Ni2.24Mn0.75Ga1.02 (x0.24) in
the FT phase is also shown.
Banik et al Phys. Rev. B, 74, 085110 2006
54
Compare with IPES spectra of Nickel and
Manganese metal
55
Calculated Spin polarized energy bands of
Ni2MnGa
Minority spin
Majority spin
A parabolic majority spin band crosses EF near
M and R points. Between -0.7 and -4 eV exhibit
small dispersion and are related to Ni 3d-Mn 3d
hybridized states. In the GX, GM or GR
direction, no majority spin bands are observed
between EF and -0.7 eV and no EF crossing is
observed. Half metallic character along certain
directions ( GX, GM and GR ) of the Brillouin
zone with a gap of about 0.7 eV Future plan
for experimental determination of band dispersion
by ARPES.
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57
Origin of the modulated phases in Ni2MnGa Fermi
surface nesting
Partial phonon dispersion of Ni2MnGa in the fcc
Heusler structure, along the G-K-X line in the
(110) direction. The experimental data taken at
250 K and 270 K.

Cross section of the minority-spin Fermi surface
(a) with the (001) plane. The arrows are examples
of nesting vectors q00.34(1,1,0).
(a) Fermi surface of cubic Ni2MnGa. (b) The fcc
BZ is shown as a reference.
Bungaro, Rabe, Dal Corso, PRB, 68, 134104, (2003)
58
Possibility of tuning the minority spin DOS near
EF
x 0.25
x 0
59
Magnetoresistance and twin variant rearrangement

• Ni2MnGa, in the martensitic phase exhibits a cusp
  like shape with two inflection points at 0.3 T
  and 1.3 T. This is due to the twinning and large
  magnetocrystalline anisotropy in the martensitic
  phase
• At 150 K, x0, x0.1 and x0.2 are at the
  martensitic phase. For x0.1, the inflection
  points are observed at lower H. For x0.2, MR is
  almost linear with a possible inflection point at
  0.15 T.

C. Biswas, R. Rawat, S.R. Barman, Appl. Phys.
Lett., 86, 202508 (2005)